Interplay Between Transmission Delay, Average Data Rate, and Performance in Output Feedback Control over Digital Communication Channels

The performance of a noisy linear time-invariant (LTI) plant, controlled over a noiseless digital channel with transmission delay, is investigated in this paper. The rate-limited channel connects the single measurement output of the plant to its single control input through a causal, but otherwise arbitrary, coder-controller pair. An infomation-theoretic approach is utilized to analyze the minimal average data rate required to attain the quadratic performance when the channel imposes a known constant delay on the transmitted data. This infimum average data rate is shown to be lower bounded by minimizing the directed information rate across a set of LTI filters and an additive white Gaussian noise (AWGN) channel. It is demonstrated that the presence of time delay in the channel increases the data rate needed to achieve a certain level of performance. The applicability of the results is verified through a numerical example. In particular, we show by simulations that when the optimal filters are used but the AWGN channel (used in the lower bound) is replaced by a simple scalar uniform quantizer, the resulting operational data rates are at most around 0.3 bits above the lower bounds.Comment: A less-detailed version of this paper has been accepted for publication in the proceedings of ACC 201

Fundamental limits in Gaussian channels with feedback: confluence of communication, estimation, and control

The emerging study of integrating information theory and control systems theory has attracted tremendous attention, mainly motivated by the problems of control under communication constraints, feedback information theory, and networked systems. An often overlooked element is the estimation aspect; however, estimation cannot be studied isolatedly in those problems. Therefore, it is natural to investigate systems from the perspective of unifying communication, estimation, and control;This thesis is the first work to advocate such a perspective. To make Matters concrete, we focus on communication systems over Gaussian channels with feedback. For some of these channels, their fundamental limits for communication have been studied using information theoretic methods and control-oriented methods but remain open. In this thesis, we address the problems of characterizing and achieving the fundamental limits for these Gaussian channels with feedback by applying the unifying perspective;We establish a general equivalence among feedback communication, estimation, and feedback stabilization over the same Gaussian channels. As a consequence, we see that the information transmission (communication), information processing (estimation), and information utilization (control), seemingly different and usually separately treated, are in fact three sides of the same entity. We then reveal that the fundamental limitations in feedback communication, estimation, and control coincide: The achievable communication rates in the feedback communication problems can be alternatively given by the decay rates of the Cramer-Rao bounds (CRB) in the associated estimation problems or by the Bode sensitivity integrals in the associated control problems. Utilizing the general equivalence, we design optimal feedback communication schemes based on the celebrated Kalman filtering algorithm; these are the first deterministic, optimal communication schemes for these channels with feedback (except for the degenerated AWGN case). These schemes also extend the Schalkwijk-Kailath (SK) coding scheme and inherit its useful features, such as reduced coding complexity and improved performance. Hence, this thesis demonstrates that the new perspective plays a significant role in gaining new insights and new results in studying Gaussian feedback communication systems. We anticipate that the perspective could be extended to more general problems and helpful in building a theoretically and practically sound paradigm that unifies information, estimation, and control

Adaptive Input Reconstruction with Application to Model Refinement, State Estimation, and Adaptive Control.

Input reconstruction is the process of using the output of a system to estimate its input. In some cases, input reconstruction can be accomplished by determining the output of the inverse of a model of the system whose input is the output of the original system. Inversion, however, requires an exact and fully known analytical model, and is limited by instabilities arising from nonminimum-phase zeros. The main contribution of this work is a novel technique for input reconstruction that does not require model inversion. This technique is based on a retrospective cost, which requires a limited number of Markov parameters. Retrospective cost input reconstruction (RCIR) does not require knowledge of nonminimum-phase zero locations or an analytical model of the system. RCIR provides a technique that can be used for model refinement, state estimation, and adaptive control. In the model refinement application, data are used to refine or improve a model of a system. It is assumed that the difference between the model output and the data is due to an unmodeled subsystem whose interconnection with the modeled system is inaccessible, that is, the interconnection signals cannot be measured and thus standard system identification techniques cannot be used. Using input reconstruction, these inaccessible signals can be estimated, and the inaccessible subsystem can be fitted. We demonstrate input reconstruction in a model refinement framework by identifying unknown physics in a space weather model and by estimating an unknown film growth in a lithium ion battery. The same technique can be used to obtain estimates of states that cannot be directly measured. Adaptive control can be formulated as a model-refinement problem, where the unknown subsystem is the idealized controller that minimizes a measured performance variable. Minimal modeling input reconstruction for adaptive control is useful for applications where modeling information may be difficult to obtain. We demonstrate adaptive control of a seeker-guided missile with unknown aerodynamics.Ph.D.Aerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/91520/1/amdamato_1.pd

Optimal Tracking Performance of MIMO Discrete-Time Systems with Network Parameters

The optimal regulation properties of multi-input and multioutput (MIMO) discrete-time networked control systems (NCSs), over additive white Gaussian noise (AWGN) fading channels, based on state space representation, are investigated. The average performance index is introduced. Moreover, the regulation performance is measured by the control energy and the error energy of the system, and fundamental limitations are obtained. Two kinds of network parameters, fading and the additive white Gaussian noise, are considered. The best attainable regulation performance limitations can be obtained by the limiting steady state solution of the corresponding algebraic Riccati equation (ARE). The simulation results are given to demonstrate the main results of the theoretical development

Modeling, Simulation and Control of Very Flexible Unmanned Aerial Vehicle

This dissertation presents research on modeling, simulation and control of very flexible aircraft. This work includes theoretical and numerical developments, as well as experimental validations. On the theoretical front, new kinematic equations for modeling sensors are derived. This formulation uses geometrically nonlinear strain-based finite elements developed as part of University of Michigan Nonlinear Aeroelastic Simulation Toolbox (UM/NAST). Numerical linearizations of both the flexible vehicle and the sensor measurements are developed, allowing a linear time invariant model to be extracted for control analysis and design. Two different algorithms to perform sensor fusion from different sensor sources to extract elastic deformation are investigated. Nonlinear least square method uses geometry and nonlinear beam strain-displacement kinematics to reconstruct the wing shape. Detailed information such as material properties or loading conditions are not required. The second method is the Kalman filter, implemented in a multi-rate form. This method requires a dynamical system representation to be available. However, it is more robust to noise corruption in sensor measurements. In order to control maneuver loads, Model Predictive Control is applied to maneuver load alleviation of a representative very flexible aircraft (X-HALE). Numerical studies are performed in UM/NAST for pitch up and roll maneuvers. Both control and state constraints are successfully enforced, while reference commands are still being tracked. MPC execution is also timed and current implementation is capable of almost real-time operation. On the experimental front, two aeroelastic testbed vehicles (ATV-6B and RRV-6B) are instrumented with sensors. On ATV-6B, an extensive set of sensors measuring structural, flight dynamic, and aerodynamic information are integrated on-board. A novel stereo-vision measurement system mounted on the body center looking towards the wing tip measures wing deformation. High brightness LEDs are used as target markers for easy detection and to allow each view to be captured with fast camera shutter speed. Experimental benchmarks are conducted to verify the accuracy of this methodology. RRV-6B flight test results are presented. System identification is applied to the experimental data to generate a SISO description of the flexible aircraft. System identification results indicate that the UM/NAST X-HALE model requires some tuning to match observed dynamics. However, the general trends predicted by the numerical model are in agreement with flight test results. Finally, using this identified plant, a stability augmentation autopilot is designed and flight tested. This augmentation autopilot utilizes a cascaded two-loop proportional integral control design, with the inner loop regulating angular rates and outer loop regulating attitude. Each of the three axes is assumed to be decoupled and designed using SISO methodology. This stabilization system demonstrates significant improvements in the RRV-6B handling qualities. This dissertation ends with a summary of the results and conclusions, and its main contribution to the field. Suggestions for future work are also presented.PHDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/144019/1/pziyang_1.pd